Multiplication table of Tetrahedral group.

tetrahedral_group.scala

  val id = "ABCD"                           //> id  : String = ABCD
	val tl = "BADC"                           //> tl  : String = BADC
	val tm = "DCBA"                           //> tm  : String = DCBA
	val tn = "CDAB"                           //> tn  : String = CDAB
	val a1 = "ACDB"                           //> a1  : String = ACDB
	val a2 = "ADBC"                           //> a2  : String = ADBC
	val b1 = "DBAC"                           //> b1  : String = DBAC
	val b2 = "CBDA"                           //> b2  : String = CBDA
	val c1 = "BDCA"                           //> c1  : String = BDCA
	val c2 = "DACB"                           //> c2  : String = DACB
	val d1 = "CABD"                           //> d1  : String = CABD
	val d2 = "BCAD"                           //> d2  : String = BCAD

	val ss = List(id,tl,tm,tn,a1,a2,b1,b2,c1,c2,d1,d2)
	
	val ks = List("id","tl","tm","tn","a1","a2","b1","b2","c1","c2","d1","d2")
	
	def mapping(s:String) = {
		(c: Char) => {
			c match {
				case 'A' => s.charAt(0)
				case 'B' => s.charAt(1)
				case 'C' => s.charAt(2)
				case 'D' => s.charAt(3)
		  }
		}
	}

	def comp(f:String, g:String) = {
		def mf = mapping(f)
		def mg = mapping(g)
		
		{for (c <- "ABCD".toList) yield mg(mf(c))}.mkString
	}

	for (g <- ss) {
		for (f <- ss) {
			print( ks(ss.indexOf(comp(f,g))) + " ")
		}
		println
	}